Some Energy Properties of Yang-Mills Connections

Abstract

We consider a vector bundle $E$ over a compact Riemannian manifold $M$=$M^n$,$n\ge 4$,and $A$ is a Yang-Mills connection with $L^{\frac{n}{2}}$ curvature $F_A$ on $E$.Then we prove a mean value inequality for the density $|F_A{|}^{\frac{n}{2}}$.This inequality give rise to an energy concentrate principle for sequences of solutions that have bounded energy.We also proof that the energy must be bounded from below by some positive constant unless $E$ is a flat bundle.

This paper has been withdrawn. The result of this paper turned out to be a special case of arXiv:1502.00668

Cited by in corpus (1)

• Energy gap for Yang-Mills connections, II: Arbitrary closed Riemannian manifolds